Solve the following system of equations: y = -4x + 3 y = -3x - 4
Understand the Problem
The question shows a system of two linear equations. The problem is to solve for the variables x and y. Several methods can be used, such as substitution, elimination, or graphing.
Answer
$x = 7$, $y = -25$
Answer for screen readers
$x = 7$, $y = -25$
Steps to Solve
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Set the equations equal to each other Since both equations are solved for $y$, we can set them equal to each other: $$-4x + 3 = -3x - 4$$
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Solve for $x$ Add $4x$ to both sides: $$3 = x - 4$$ Then, add $4$ to both sides: $$7 = x$$ So, $x = 7$.
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Solve for $y$ Substitute $x=7$ into either of the original equations. Let's use the first equation: $$y = -4(7) + 3$$ $$y = -28 + 3$$ $$y = -25$$
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State the solution The solution is $x = 7$ and $y = -25$.
$x = 7$, $y = -25$
More Information
We can verify the answer by plugging in $x = 7$ into the second equation: $y = -3(7) - 4 = -21 - 4 = -25$ Since both equations give us the same $y$ value for $x = 7$, the solution is correct.
Tips
A common mistake is making errors when solving the system through substitution or elimination, which will lead to the wrong values for $x$ and $y$. Another mistake is to only solve for one variable and forget to solve for the other. Remember to always solve for both $x$ and $y$ to fully answer the question!
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